# Worksheet on Remainder Theorem

Practice the questions given in the worksheet on Remainder Theorem.

1. Use the Remainder Theorem, find the remainder when 4x$$^{3}$$ - 3x$$^{2}$$ + 2x - 4 is divided by x + 1.

2. If p(y) = y$$^{3}$$ + y$$^{2}$$ - 2y + 1, using Remainder Theorem, find the remainder, when p(y) is divided by (y – 3), find the value of p(a).

3. Find the remainder (without division) when

(a) x$$^{2}$$ - 2x + 4 is divided by x - 1

(b) 2x$$^{3}$$ - 3x$$^{2}$$ + 7x - 8 is divided by x - 1

4. Use the Remainder Theorem, find the remainder when x$$^{4}$$ - 3x$$^{2}$$ + 4x - 12 is divided by x - 3.

5. Find the remainder (without division) when

(a) x$$^{3}$$ + 4x + 2 is divisible by x + 2

(b) 4x$$^{3}$$ - 3x$$^{2}$$ + 5x + 4 is divided by 2x + 1

(c) 4x$$^{3}$$ + 5x$$^{2}$$ + 6x - 7 is divided by 2x - 1

6. What number should be added to x$$^{2}$$ + 5 so that the resulting polynomial leaves the remainder 3 when divided by x + 3?

7. Use the Remainder Theorem, find the remainder when 4x$$^{3}$$ - 3x$$^{2}$$ + 2x - 4 is divided by x + 1.

8. What number should be subtracted from 3x$$^{2}$$ + 5x so that the resulting polynomial leaves the remainder 1 when divided by 2x + 5?

9. Use the Remainder Theorem, find the remainder when x$$^{6}$$ + 3x$$^{2}$$ + 10 is divided by x - 2.

10.  Find a if the remainder is a when x$$^{3}$$ + 3x$$^{2}$$ - ax + 3 is divided by x - 2.

11. If the polynomials ax$$^{3}$$ + 4x$$^{2}$$ + 3x – 4 and x$$^{3}$$ - 4x + a leave the same remainder when divided by (x - 3), find the value of a.

12. Find the value of k if the remainder is -3 when kx$$^{3}$$ + 8x$$^{2}$$ - 4x + 10 is divided by x +1.

13. If both ax$$^{3}$$ + 2x$$^{2}$$ - 3 and x$$^{2}$$ - ax + 4 leave the same remainder when divided by x - 2, find a.

Answers for the worksheet on Remainder Theorem are given below:

1. -13

2. 31, a$$^{3}$$ + a$$^{2}$$ - 2a + 1

3. (a) 3

(b) -2

4. 54

5. (a) -14

(b) $$\frac{1}{4}$$

(c) -$$\frac{9}{4}$$

6. -11

7. -13

8. $$\frac{21}{4}$$

9. 86

10. $$\frac{23}{3}$$

11. a = -1.

12. 25

13. $$\frac{3}{10}$$

● Factorization

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